Optimal Solution of the Maximum All Request Path Grooming Problem

  • Authors:

  • Jean-Claude Bermond;Michel Cosnard;David Coudert;Stephane Perenn

  • Affiliations:

  • CNRS/I3S/INRIA, Cedex France;CNRS/I3S/INRIA, Cedex France;CNRS/I3S/INRIA, Cedex France;CNRS/I3S/INRIA, Cedex France

  • Venue:
  • AICT-ICIW '06 Proceedings of the Advanced Int'l Conference on Telecommunications and Int'l Conference on Internet and Web Applications and Services
  • Year:
  • 2006

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Abstract

We give an optimal solution to the Maximum All Request Path Grooming (MARPG) problem motivated by a traffic grooming application. The MARPG problem consists in finding the maximum number of connections which can be established in a path of size N, where each arc has a capacity or bandwidth C (grooming factor). We present a greedy algorithm to solve the problem and an explicit formula for the maximum number of requests that can be groomed. In particular, if C = s(s+1)/2 and N \ge s(s-1), an optimal solution is obtained by taking all the requests of smallest length, that is of length 1 to s. However this is not true in general since anomalies can exist. We give a complete analysis and the exact number of such anomalies.